G is a digraph with edge costs and capacities and in which nodes
have demand, i.e., they want to send or receive some amount of
flow. A negative demand means that the node wants to send flow, a
positive demand means that the node want to receive flow. A flow on
the digraph G satisfies all demand if the net flow into each node
is equal to the demand of that node.

Parameters:

G (NetworkX graph) – DiGraph on which a minimum cost flow satisfying all demands is
to be found.

demand (string) – Nodes of the graph G are expected to have an attribute demand
that indicates how much flow a node wants to send (negative
demand) or receive (positive demand). Note that the sum of the
demands should be 0 otherwise the problem in not feasible. If
this attribute is not present, a node is considered to have 0
demand. Default value: ‘demand’.

capacity (string) – Edges of the graph G are expected to have an attribute capacity
that indicates how much flow the edge can support. If this
attribute is not present, the edge is considered to have
infinite capacity. Default value: ‘capacity’.

weight (string) – Edges of the graph G are expected to have an attribute weight
that indicates the cost incurred by sending one unit of flow on
that edge. If not present, the weight is considered to be 0.
Default value: ‘weight’.

Returns:

flowDict – Dictionary of dictionaries keyed by nodes such that
flowDict[u][v] is the flow edge (u, v).

Return type:

dictionary

Raises:

NetworkXError – This exception is raised if the input graph is not directed or
not connected.

NetworkXUnfeasible – This exception is raised in the following situations:

The sum of the demands is not zero. Then, there is no
flow satisfying all demands.

There is no flow satisfying all demand.

NetworkXUnbounded – This exception is raised if the digraph G has a cycle of
negative cost and infinite capacity. Then, the cost of a flow
satisfying all demands is unbounded below.

This algorithm is not guaranteed to work if edge weights or demands
are floating point numbers (overflows and roundoff errors can
cause problems). As a workaround you can use integer numbers by
multiplying the relevant edge attributes by a convenient
constant factor (eg 100).